## Principal Component AnalysisPrincipal component analysis is central to the study of multivariate data. Although one of the earliest multivariate techniques it continues to be the subject of much research, ranging from new model- based approaches to algorithmic ideas from neural networks. It is extremely versatile with applications in many disciplines. The first edition of this book was the first comprehensive text written solely on principal component analysis. The second edition updates and substantially expands the original version, and is once again the definitive text on the subject. It includes core material, current research and a wide range of applications. Its length is nearly double that of the first edition. Researchers in statistics, or in other fields that use principal component analysis, will find that the book gives an authoritative yet accessible account of the subject. It is also a valuable resource for graduate courses in multivariate analysis. The book requires some knowledge of matrix algebra. Ian Jolliffe is Professor of Statistics at the University of Aberdeen. He is author or co-author of over 60 research papers and three other books. His research interests are broad, but aspects of principal component analysis have fascinated him and kept him busy for over 30 years. |

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### Contents

Principal Components 2 2 Geometric Properties of Population Principal Components | 2 |

Graphical Representation of Data Using | 78 |

2 | 85 |

5 | 99 |

6 | 105 |

Choosing a Subset of Principal Components or Variables | 111 |

Principal Component Analysis and Factor Analysis | 150 |

Principal Components in Regression Analysis | 167 |

Principal Components Used with Other Multivariate | 199 |

Outlier Detection Influential Observations and Robust Estimation | 232 |

Detection of Outliers Using Principal Components 10 1 1 Examples 10 2 Influential Observations in a Principal Component Analysis 10 2 1 Example... | 269 |

Rotation of Principal Components 11 1 1 Examples 11 1 2 Onestep Procedures Using Simplicity Criteria 11 2 Alternatives to Rotation 11 2 1 Compo... | 300 |

Principal Component Analysis for Special Types of Data | 338 |

Generalizations and Adaptations of Principal | 373 |

A Computation of Principal Components | 406 |

63 | 418 |

424 | |

435 | |

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### Common terms and phrases

algorithm approximation biplot canonical correlation analysis Chapter cluster coefficients columns compared computational constraints context correlation matrix correspondence analysis covariance matrix covariance or correlation criterion data matrix data set decomposition defined deleted derived described detect diagonal discriminant analysis discussed in Section distance distribution eigenvalues eigenvectors elements EOFs equation example factor analysis Flury give given groups idea influence function instrumental variables interpretation Jolliffe Krzanowski last few PCs linear functions loadings Mahalanobis distance maximize measurements method minimize multivariate normal multivariate normal distribution neural network non-linear optimal original variables orthogonal outliers p-dimensional PC regression PC scores plot possible prediction predictor variables principal component analysis principal curves procedure projection pursuit properties respect similar singular value decomposition spatial Statist structure subspace suggested Table technique tion total variation transformation uncorrelated values variance vector weights zero